The ducts being on the port side only presumably indicates the air conditioning is driven from the port engine.
Not so - that was one of the factors that lead to the Kegworth crew shutting down the wrong engine. They smelt smoke on the flightdeck and thought it was only supplied by one engine - so shut that engine down. On later 737s, including the -400 (not covered in their conversion training), both engines supply the air conditioning packs.